The student produces evidence that demonstrates
understanding of statistics and probability concepts in the following
areas; that is, the student: |
 a
Collects and organizes data to answer a question or test a hypothesis
by comparing sets of data.
|
b
Displays data in line plots, graphs, tables, and charts.
|
| c
Makes statements and draws simple conclusions
based on data; that is: |
| • |
reads data in line plots, graphs, tables, and charts; |
| • |
compares data in order to make true statements, e.g., “seven
plants grew at least 5 cm”; |
| • |
identifies and uses the mode necessary for making true statements,
e.g., “more people chose red”; |
| • |
makes true statements based on a simple concept of average (median
and mean), for a small sample size and where the situation is made
evident with concrete materials or clear representations; |
| • |
interprets data to determine the reasonableness of statements about
the data, e.g., “twice as often,” “three times faster”; |
| • |
uses data, including statements about the data, to make a simple
concluding statement about a situation, e.g., “This kind of
plant grows better near sunlight because the seven plants that were
near the window grew at least 5 cm.”
|
d
Gathers data about an entire group or by sampling
group members to understand the concept of sample, i.e., that a large
sample leads to more reliable information, e.g., when flipping coins.
|
e
Predicts results, analyzes data, and finds out why some results are
more likely, less likely, or equally likely.
|
| e
Finds all possible combinations and arrangements
within certain constraints involving a limited number of variables. |
The
student produces evidence that demonstrates understanding of statistics
and probability concepts; that is, the student: |
a
Collects data, organizes data, and displays
data with tables, charts, and graphs that are appropriate, i.e., consistent
with the nature of the data.
|
b
Analyzes data with respect to characteristics
of frequency and distribution, including mode and range.
|
c
Analyzes appropriately central tendencies of
data by considering mean and median.
|
d
Makes conclusions and recommendations based
on data analysis.
|
e
Critiques the conclusions and recommendations
of others’ statistics.
|
f
Considers the effects of missing or incorrect
information.
|
g
Formulates hypotheses to answer a question
and uses data to test hypotheses.
|
h
Represents and determines probability as a
fraction of a set of equally likely outcomes; recognizes equally likely
outcomes, and constructs sample spaces (including those described
by numerical combinations and permutations).
|
i
Makes predictions based on experimental or
theoretical probabilities.
|
j
Predicts the result of a series of trials once the probability for
one trial is known.
|
The student demonstrates understanding of
statistics and probability concepts; that is, the student: |
a
Organizes, analyzes, and displays single-variable
data, choosing appropriate frequency distributions, circle graphs,
line plots, histograms, and summary statistics.
|
b
Organizes, analyzes, and displays two-variable
data using scatter plots, estimated regression lines, and computer
generated regression lines and correlation coefficients.
|
c
Uses sampling techniques to draw inferences
about large populations.
|
d
Understands that making an inference about
a population from a sample always involves uncertainty and that the
role of statistics is to estimate the size of that uncertainty.
|
e
Formulates hypotheses to answer a question
and uses data to test hypotheses.
|
f
Interprets representations of data, compares
distributions of data, and critiques conclusions and the use of statistics,
both in school materials and in public documents.
|
g
Explores questions of experimental design,
use of control groups, and reliability.
|
h
Creates and uses models of probabilistic situations
and understands the role of assumptions in this process.
|
i
Uses concepts such as equally likely, sample
space, outcome, and event in analyzing situations involving chance.
|
j
Constructs appropriate sample spaces, and applies
the addition and multiplication principles for probabilities.
|
k
Uses the concept of a probability distribution
to discuss whether an event is rare or reasonably likely.
|
l
Chooses an appropriate probability model and
uses it to arrive at a theoretical probability for a chance event.
|
m
Uses relative frequencies based on empirical
data to arrive at an experimental probability for a chance event.
|
n
Designs simulations including Monte Carlo simulations
to estimate probabilities.
|
o
Works with the normal distribution in some
of its basic applications.
|
|
Statistics and Probability Concepts